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30 Jan 2014, 23:48
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C
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Difficulty:
15%
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Question Stats:
77% (01:24) correct
23%
(01:30)
wrong
based on 2909
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K is a set of numbers such that
(i) if x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K.
Is 12 in K?
(1) 2 is in K.
(2) 3 is in K.
(i) if x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K.
Is 12 in K?
(1) 2 is in K.
(2) 3 is in K.
30 Jan 2014, 23:48
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SOLUTION
K is a set of numbers such that
(i) if x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K.
Is 12 in K?
(1) 2 is in K --> according to (i) -2 is n K --> according to (ii) -2*2=-4 is in K --> according to (i) -(-4)=4 is in K and so on. Thus we know that 2, -2, -4, 4, 8, -8, 16, -16, ... are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient.
(2) 3 is in K --> according to (i) -3 is n K --> according to (ii) -3*3=-9 is in K --> according to (i) -(-9)=9 is in K and so on. Thus we know that 3, -3, -9, 9, 27, -27, 81, -81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don't know. Not sufficient.
(1)+(2) From (1) 4 is in K and from (2) 3 is in K, hence according to (ii) 4*3=12 must also be in K. Sufficient.
Answer: C.
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Hope this helps.
K is a set of numbers such that
(i) if x is in K, then -x is in K, and
(ii) if each of x and y is in K, then xy is in K.
Is 12 in K?
(1) 2 is in K --> according to (i) -2 is n K --> according to (ii) -2*2=-4 is in K --> according to (i) -(-4)=4 is in K and so on. Thus we know that 2, -2, -4, 4, 8, -8, 16, -16, ... are in K, so basically powers of 2 and their negative pairs. Is 12 in K? We don't know. Not sufficient.
(2) 3 is in K --> according to (i) -3 is n K --> according to (ii) -3*3=-9 is in K --> according to (i) -(-9)=9 is in K and so on. Thus we know that 3, -3, -9, 9, 27, -27, 81, -81, ... are in K, so basically powers of 3 and their negative pairs. Is 12 in K? We don't know. Not sufficient.
(1)+(2) From (1) 4 is in K and from (2) 3 is in K, hence according to (ii) 4*3=12 must also be in K. Sufficient.
Answer: C.
Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
Hope this helps.
General Discussion
19 Feb 2014, 07:01
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Bunuel, one quick query -> When we say that (from stmt 1) 2 is there in the set and hence -2 is also there -> Here we take 2 and -2 as x and -x, but then we also apply the logic x*y = -4 (here we consider 2 as x and -2 as y (and not as -x)).
Could there be a flaw in the problem statement?
Could there be a flaw in the problem statement?
Bunuel
